Describe the long run behavior of f(t) = – 2(5)' – 3 | As t → - 0, f(t) → ? v As t → 0, f(t) → ? v

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: A particle is moving along a line, whose directed distance from its origin is given by the function…

A: f(t) is a distance function.

Q: af Q1: a) Use the chain rule to calculate for the function f(x, y, z) = 3x² - 3y + 4xz², x =…

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Q: The function f defined by the rule f(z, y) = In(xy) increases fastest in the direction of T. F (1,…

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

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A: Given problem:- Find laplace transformation of f(t) =et (0<t<2π)

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Q: Find the minimum and maximum of A over a particular interval [0,6]. A(x) = f(t) dt

A: The solution is given below in the next step: I

Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

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Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

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Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: Consider the following equation: w=x2+y2 Substitute x=cost+sint and y=cost-sint in the above…

Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: 1 Find f(1) if f(t) dt = x" - x + 2x? – 2, x >1.

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Q: 1losamlov ç5x3-1 Differentiate the function g(x) = [°*¯'sin t dt. -3

A: We have to differentiate the given function.

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

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Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

Q: Find the linearization of the function f (x) = xº at x = 1. L (x) = Using this linearlization, f…

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Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

Q: Recall the chain rule from differential calculus: f (g (æ)) = f' (9 (æ)) · g' (æ). d dx Find de tan…

A: We have to find

Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: 6. If F(x) is defined by cx²+2x esin(t) dt F(x) = Determine F'(x).

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Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

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Q: (b) Prove that sint -dt > 0 t+1 for all a > 0.

A: Given:- ∫0x sintt+1dt >0

Q: 1 Let H(s) Using convolution to find h(t) s2 (s-a)

A: Inverse Laplace transferom

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

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Q: Let Dx be the linear transformation from C'[a, b] into Cla, b]. Find the preimage of the function.…

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Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: Suppose fn → f and the functions fn all satisfy the Lipschit condition |fn(x) – fn(y)| < Mx – y| for…

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Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 3n/2 %3D

A: We have to find the linearization L(x) of the given function.

Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

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Q: 2. Suppose that z is a function of a and y, and F(x2 - y², xy - 2², yz - 2²) = 0. Calculate and…

A: Solution :

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

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Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

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Q: Q2/ Express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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